One who dies believing in Islaam
without converting

Non-muslim dies, and I know
him/her. As far as I know this person beleived and accepted
Islam, but died before they could convert. What does Islam
say about such a person, is he/she forgiven by Allah or still
considered as one of the "kaffar"?

Praise be to
Allaah.

If a person does not pronounce the Shahaadatayn and enter
Islaam, we cannot say that he is a Muslim, even if he admired
Islaam and recognized that it the best religion, a great
religion, and so on. Abu Taalib, the uncle of the Prophet died a kaafir, and Allaah forbade His Prophet to
pray for forgiveness for him, even though he used to defend
the Prophet and said in his poems:
"I do know that the religion of Muhammad is better than
all other religions of mankind;
were it not for fear of blame or slander, you would find me
accepting it completely."

If a person accepts Islaam out of conviction, and begins to
practise it, then he is a Muslim, even if he does not
register his Islaam officially, or go to a court or Islaamic
centre to obtain documentation, or announce it to others. If
such a person dies, then we hope for Paradise for him and
pray for mercy for him.